The minimum requirements to now feel up or view naked, you, your wife and your kids.
Educational Background
FAR 108.31(a)(1) requires that screeners possess a high school diploma, a General Equivalency Diploma, or a combination of education and experience which the certificate holder has determined to have equipped the person to perform the duties of the position. This implies that the airline can decide that a screener does not have to successfully complete high school.
Criminal Background Checks
FAR 108.33(c)(5) does not require criminal records checks for every screener applicant, only for those applicants who have specific deficiencies in their employment history, if there are other deficiencies in the application, or if the air carrier finds out that the applicant may have been convicted of certain kinds of crimes. The required criminal records check is with the FBI, but the regulations do not say anything about records checks from other countries.
Criminal History
Surprisingly, a conviction for a crime, even a violent felony, does not disqualify someone from working as a screener. FAR 108.33(2) states that a criminal records check must not disclose that the applicant had been convicted or found not guilty by reason of insanity, in any jurisdiction, during the previous 10 years of a number of crimes such as aircraft piracy, interference with a flight crew or cabin crew member, assault with intent to murder, rape or aggravated sexual abuse, or armed robbery. This list of crimes include sedition, treason, extortion, or distribution of a controlled substance. This regulation implies that so long as the conviction were at least 10 years old, almost any convicted criminal could become a security screener.